"If you create a machine to do the job of a man, you take something away from the man."

Don't get me wrong... I am not technology averse, nor do I entirely agree with the statement above.  It is, after all, only a quote from a mediocre STAR TREK movie.  A person's philosophy on life and existence should not be shaped and molded by a simple quote.  However, there is a fundamental danger in technology which gives this quote a small ring of truth.  Here's what I am getting at...

Technology comes into our lives a little bit at a time.  At first, it is novel, something to keep you ahead of the Joneses, then it becomes ubiquitous, then it becomes essential, then no one alive can remember a time without it.  Technology has allowed man (I use the term for convenience, not out of any misogynist tendencies) to do many wonderful things that he could never do otherwise.  Humans can't fly except through the use of technology, and the airplane has shrunk the world to only a day's travel from anywhere to anywhere else; Locomotives united east and west in the United States; the remote control fundamentally changed how we watch television, as did the VCR and the DVD player; computers, a thing of wonder relegated to classrooms and university labs merely 25 years ago, can now be worn on your wrist by anyone anywhere.  Can any of us imagine life without any of these technological advances?  Yet, for each one of these, there was a time when we did without them because they simply did not exist. 

When I was in high school, it seems like a foolish thing now, but calculators were hotly debated.  Were they a helpful tool to the math educator or an easy way out for the lazy math student?  There were specific rules that some of my math teachers had as to what qualified as an acceptable calculator problem.  This was usually when the math was long, ugly, complicated and prone to mistakes.  If you were caught walking into an SAT test with a calculator, including the wristwatches with the calculator built in, at the very least it would have been confiscated, and at worst you would have been asked to leave.  Yet now calculators are practically mandatory for an SAT test.  I have seen students pull out their calculators (including my own 11-year old daughter) to calculate things as simple as 35 divided by 5!  Or even easier, anything times ten!!  In greater and greater numbers our math students are relegating the basic skills to a machine, yet there is no great advancement in the complexity of the math being learned.  Students still graduate from high school having learned basic calculus, if they are the elite.  We have taken away part of the man, and replaced it with nothing greater.

The laptop and ipad are the contemporary equivalent of calculators of my generation.  We have certainly been privy to a parade of nifty things, such as Desmos and Geogebra and 101qs, that the computer allows us to utilize in teaching mathematics.  But are we as math educators on the slippery slope that allows the machine to do the job of a teacher?  One must never forget that behind every math game and math activity is the word "MATH".

What are we to do when the technology fails us?  Now, I am not referring to a doomsday apocalypse or global EMPs frying all electronics.  Learning disasters can be much simpler than that.  I have witnessed more basic problems, like network connectivity issues or forgotten passwords, that caused entire class periods of math instruction to be wasted not only because the teacher kept trying desperately to solve the issue, but because the teacher seemed unable (or perhaps just unwilling) to, for lack of a better term, teach math the old fashioned way.  This is eerily similar to the bright student who pulls out the calculator when they are perfectly capable of solving the problem themselves.  As technology becomes so integral to education that it becomes essential, a teacher must be vigilant to not become like his or her students and rely on technology exclusively to do all the educating for them.  Always the learning must show the mathematical truths that are at the foundation.  Otherwise we are only teaching how to play a game or use a program without critical thinking.  This is not the path to innovation and advancement; it is the path to indifference and apathy.

Computers in classrooms are here to stay.  Soon the day will arrive when no one alive will remember a time without computers and acers and ipads as an integral part of learning and teaching.  Let us all strive to make sure that they are a tool to open up doorways to rooms of knowledge and learning that we only dreamed of entering, that the next generation has a better grasp of math than we did, that they do not simply relegate math to the machines.  Because when that happens, we truly TRULY will not be able to do for ourselves, and something vital will have been taken away from us indeed!

Developing Students' Understanding of a Variable, by Ana C. Stephens.

This article deals with helping secondary students fully grasp the concept of a variable.  Three secondary classroom teachers were given a mouse thought exercise, where one has to come up with all the various ways that eight mice can be shared between two mouse cages connected by a tunnel.  Students developed charts, tables, even pictures to represent the ways, and they were encouraged to figure out a way to express this concept algebraically.  What struck me most was that so many students could not accept openly that two separate variables, say m and n, could share the same value.  This opens up my deeper concern for myself as a secondary math teacher: because so many math concepts have always come so easily to me, how much will I struggle in adapting concepts to make them more easily assimilated by the average or below average math student.  I recall in my elementary school days that we had math problems to do of the variety, __ + 5=8, and we had to figure out what went in the blank.  Then in middle school the blank was replaced with a letter, a variable, and this was an easy transition for me to make.  When this transition is a difficult one for a student in my classroom, I am hopeful that I will be both creative and understanding enough to allow the student to grasp the concept without completely being turned off by math.